Number Theory in Mathematics Education

<p>This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature its relation to arithmetic and algebra its accessibility its utility and intrinsic merits to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that collectively make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education.<br><br>Topics variously engaged include:<br>*understanding particular concepts related to numerical structure and number theory;<br>*elaborating on the historical and psychological relevance of number theory in concept development;<br>*attaining a smooth transition and extension from pattern recognition to formative principles;<br>*appreciating the aesthetics of number structure;<br>*exploring its suitability in terms of making connections leading to <i>aha!</i> insights and reaching toward the learner's affective domain;<br>*reexamining previously constructed knowledge from a novel angle;<br>*investigating connections between technique and theory;<br>*utilizing computers and calculators as pedagogical tools; and<br>*generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers.<br><br>Overall the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism and as a means for providing intuitively grounded meanings of numbers variables functions and proofs.<br><br><i>Number Theory in Mathematics Education: Perspectives and Prospects</i> is of interest to researchers teacher educators and students in the field of mathematics education and is well suited as a text for upper-level mathematics education courses.</p>